Jeremy Corbyn has called on Theresa May to rethink the troubled universal credit benefits system and abolish the charge for its helpline, which costs frustrated claimants up to 55p a minute to call from a mobile phone.

The pair clashed on the issue of welfare in May’s first prime minister’s questions since her disastrous conference speech, which led to an attempted coup against her leadership by the former party chairman Grant Shapps.

With her position still under threat, the SNP also mocked May for failing to say whether she would vote for Brexit in another referendum, and she was challenged by some of her own backbenchers over whether she was sufficiently preparing for leaving the EU with no deal.

Corbyn chose to direct his questions to May largely on the subject of difficulties with universal credit, a new system that rolls six benefits into a single monthly payment. The Labour leader pointed out that some claimants have had to wait more than six weeks for their first payments.

He called for the prime minister to “show some humanity” by making the helpline that assists claimants who have problems with universal credit free.

May said “changes have been made, and performance has increased” following concerns that people were having to borrow and fall into rent arrears because of delays with payments.

“For example, at the beginning of this year only 55% of people were getting their first payment on time, [now] that is over 80%,” she said. “Of course there is more for us to do and that’s why the Department for Work and Pensions continues to monitor this and continue to ensure the performance increases.”

Heidi Allen, a Conservative MP, added to concerns, saying there were many on the government’s benches who believed changes were needed. May defended the principle of universal credit and argued it was incentivising people to work more, but agreed to have a meeting with Allen.

The prime minister’s spokesman defended the helpline, saying people worried about the cost could ask for a call back from the DWP.

Corbyn said universal credit was one of a “string of failures of this government”. If May was unable to resolve them, she should resign, he said.

“Everywhere you look it’s a government in chaos. On the most important issues facing this country it’s a shambles,” he said. “Brexit negotiations made no progress. Bombardier and other workers facing redundancy. Most working people worse off. Young people pushed into record levels of debt. A million elderly people not getting essential care. Our NHS at breaking point.

“This government is more interested in fighting amongst themselves than in solving these problems … Isn’t it the case that if a prime minister can’t lead she should leave?”

May defended the government’s record on the deficit, jobs, schools and the NHS before criticising Labour’s policy of setting rent controls, which the housing charity Shelter has said could harm people on low incomes.

She also attacked Labour over accusations of antisemitism, saying: “The Equality and Human Rights Commission said Labour needs to establish it is not a racist party and the Labour leader of Brighton council threatened to ban Labour conferences because of freely expressed antisemitism.

“And that was all before the shadow chancellor admitted a Labour government would bring a run on the pound, and ordinary working people would pay the price.”

Ian Blackford, the SNP leader in Westminster, subsequently mocked the prime minister for her refusal to say whether she would vote to leave the EU if there were another referendum.

May, who voted to remain in the 2016 poll, said in an interview on Tuesday that she would have to weigh up the evidence, and told Blackford the question was irrelevant because there would not be another referendum.

“There is no second referendum. The people of the United Kingdom voted and we will be leaving the European Union in March 2019,” she said.

Liz Truss, a Treasury minister, said she had changed her mind about Brexit and would now vote to leave.

She told BBC2’s Daily Politics: “All of us had to make a judgment on what we thought the future would look like. I made a judgment thinking it would be bad for the economy. Since we have left, it has been more positive, so the facts have changed and I have changed my mind.

“No forecast is completely accurate. No one has a crystal ball. I believed that there would be major economic problems. Those haven’t come to pass and I have also seen the opportunities.

“The other thing is that there was a big moment on 23 June when British people voted to leave and it was an expression about what kind of country we wanted to be. I think that has changed the debate in this country as well.”